Question: $-10bd + 3c + 5d - 5 = -5c - d - 7$ Solve for $b$.
Solution: Combine constant terms on the right. $-10bd + 3c + 5d - {5} = -5c - d - {7}$ $-10bd + 3c + 5d = -5c - d - {2}$ Combine $d$ terms on the right. $-10bd + 3c + {5d} = -5c - {d} - 2$ $-10bd + 3c = -5c - {6d} - 2$ Combine $c$ terms on the right. $-10bd + {3c} = -{5c} - 6d - 2$ $-10bd = -{8c} - 6d - 2$ Isolate $b$ $-{10}b{d} = -8c - 6d - 2$ $b = \dfrac{ -8c - 6d - 2 }{ -{10d} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $b = \dfrac{ {4}c + {3}d + {1} }{ {5d} }$